Complete Convergence of Competitive Neural Networks with Different Time Scales

This paper studies the complete convergence of a class of neural networks with different time scales under the assumption that the activation functions are unsaturated piecewise linear functions. Under this assumption, there are multiple equilibrium points in the neural network. Traditional methods cannot be used in this neural network. Complete convergence is proved by constructing an energy-like function. Simulations are employed to illustrate the theory.     

Passivity and robust synchronisation of switched interval coupled neural networks with time delay

This paper is concerned with passivity and robust synchronisation of switched coupled neural networks with uncertain parameters. First, the mathematical model of switched coupled neural networks with interval uncertain parameters is established, which consists of L modes and switches from one mode to another according to the switching rule. Second, by employing passivity theory and linear matrix inequality techniques, delay-independent and delay-dependent conditions are derived to guarantee the passivity of switched interval coupled neural networks. Moreover, based on the proposed passivity results, global synchronisation criteria can be obtained for switched coupled neural networks with or without uncertain parameters. Finally, an illustrative example is provided to demonstrate the effectiveness of the obtained results.     

Dynamic Analysis of Stochastic Recurrent Neural Networks

This paper addresses the issue of pth moment exponential stability of stochastic recurrent neural networks (SRNN) with time-varying interconnections and delays. With the help of the Dini derivative of the expectation of V(t, X(t)) “along” the solution X(t) of the model and the technique of Halanay-type inequality, some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established. Conclusions of the development as presented in this paper have gone beyond some published results and are helpful to design stability of networks when stochastic noise is taken into consideration. An example is also given to illustrate the effectiveness of our results.     

Passivity analysis for uncertain BAM neural networks with time delays and reaction–diffusions

This article deals with the problem of passivity analysis for delayed reaction–diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.     

带两个不同时延神经网络的稳定性研究

讨论了带两个不同时延且有两个神经元系统的局部稳定性,得到了判定神经网络稳定性的一些准则,这些准则有的是与时延有关,而有的是与时延无关（这种情形也称为“无害时延”）;研究方法对于带不同时延且多个神经元网络的稳定性的研究有重要的指导意义。     

随机Hopfiedld神经网络的稳定性分析

通过利用动态大规模互连系统的分解方法,对由Ｉｔｏ随机微分方程描述的随机Ｈｏｐｆｉｌｅｄ神经网络给出了稳定性分析,这样的神经网络被认为是许多神经元的一个互连,在本文中给出了稳定性结论是以单个神经凶和互连结构的性质来表示的。     

无穷时滞神经网络的全局稳定性

本文研究具有无穷时滞的神经网络的全局稳定性问题。通过拓广泛函数微分方程理论中的Ｒａｚｕｍｉｋｈｉｎ思想，获得了无十分简洁的稳定性准则。     

应用无源性分析时变非线性系统的稳定性

应用无源性分析研究时变非线性系统的稳定性.通过引进一个非线性复合微分算子dI(x)=k(x)s和一个时变非线性复合微分算子dLI(x,t)=k(x,t)sk(x,t),讨论了基于无源系统理论的时变非线性系统的稳定性分析.这里s=d/dt为普通的微分算子,x为所研究系统的状态变量.应用复合微分算子,构造出了一类严格无源的时变非线性系统,进一步给出了相应系统的渐近稳定条件.     

时滞脉冲型Hopfield神经网络的全局指数稳定性*

基于众多领域及生物神经网络本身所存在的脉冲瞬动现象，本文首次提出并研究了带时滞的脉冲型Ｈｏｐｆｉｅｌｄ神经网络的全局指定稳定性问题，并讨论了其平衡态的存在唯一性。     

基于LMI方法的时滞细胞神经网络稳定性分析

神经网络是一个复杂的大规模非线性系统,而时滞神经网络的动态行为更为丰富和复杂．现有的研究时滞神经网络稳定性的方法中最为流行的是Lyapunov方法．它把稳定性问题变为某些适当地定义在系统轨迹上的泛函,通过这些泛函相应的稳定性条件就可以获得．该文得到了时滞细胞神经网络渐近稳定性的一些充分条件．作者利用了泛函微分方程的Lyapunov—Krasovskii稳定性理论和线性矩阵不等式(LMI)方法,精炼和推广了一些已有的结果．它们比目前文献报道的结果更少保守．该文还给出了确定时滞细胞神经网络稳定性更多的判定准则．     

基于神经元网络的问句组块分析

问句分析是自动问答系统研究中的重点和难点。在中文问句的结构特点基础上,结合机器学习及组块分析理论,对问句进行组块分析,实现了基于神经网络的问句组块识别算法,并应用于银行领域自动问答系统中。测试结果表明,对问句组块的识别能够达到比较满意的效果。     

离散Hopfield-型神经网络的动态行为

主要利用网络的状态转移方程和定义能量函数的方法对非对称离散Hopfield神经网络在并行演化方式的动力学行为进行了研究。同时,给出了一些新的网络的收敛性条件。所获结果推广了一些已有的结论。     

一类具有变时滞的Hopfield型神经网络的全局指数稳定性

通过构造适当的Lyapunov函数,利用Halanay不等式和Young不等式,讨论一类具有变时滞的Hopfield型神经网络的全局指数稳定性.在对网络施加两个不同的神经元激励函数的条件下,导出网络全局指数稳定的一个充分条件,得到的充分条件在实际应用中易于验证,且有较小的保守性,因而对网络的应用和设计具有重要意义.最后,一个数值实例进一步验证结果的正确性.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay

This paper deals with the problem of passivity analysis for neural networks with time-varying delay, which is subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. Delay-dependent passivity condition is proposed by using the free-weighting matrix approach. These passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness of the proposed criteria.     

Lyapunov Functional Approach to Stability Analysis of Riemann‐Liouville Fractional Neural Networks with Time‐Varying Delays

This paper is concerned with the globally asymptotic stability of the Riemann‐Liouville fractional‐order neural networks with time‐varying delays. The Lyapunov functional approach to stability analysis for nonlinear fractional‐order functional differential equations is discussed. By constructing an appropriate Lyapunov functional associated with the Riemann‐Liouville fractional integral and derivative, the asymptotic stability criteria of fractional‐order neural networks with time‐varying delays and constant delays are derived. The advantage of our proposed method is that one may directly calculate the first‐order derivative of the Lyapunov functional. Two numerical examples are also presented to illustrate the validity and feasibility of the theoretical results. With the increasing of the order of fractional derivatives, the state trajectories of neural networks show that the speeds of converging toward zero solution are faster and faster.     

应用无源性分析研究时变非线性系统的稳定性

应用反馈系统的无源性分析研究一类时变非线性系统的稳定性,给出寻找连续衰减的充要条件的方法,并证明对于线性系统这种方法给出的结果和Routh判据完全一致.     

大数据分析的无限深度神经网络方法

深度神经网络(deep neural networks, DNNs)及其学习算法,作为成功的大数据分析方法,已为学术界和工业界所熟知.与传统方法相比,深度学习方法以数据驱动、能自动地从数据中提取特征(知识),对于分析非结构化、模式不明多变、跨领域的大数据具有显著优势.目前,在大数据分析中使用的深度神经网络主要是前馈神经网络(feedforward neural networks, FNNs),这种网络擅长提取静态数据的相关关系,适用于基于分类的数据应用场景.但是受到自身结构本质的限制,它提取数据时序特征的能力有限.无限深度神经网络(infinite deep neural networks)是一种具有反馈连接的回复式神经网络(recurrent neural networks, RNNs),本质上是一个动力学系统,网络状态随时间演化是这种网络的本质属性,它耦合了“时间参数”,更加适用于提取数据的时序特征,从而进行大数据的预测.将这种网络的反馈结构在时间维度展开,随着时间的运行,这种网络可以“无限深”,故称之为无限深度神经网络.重点介绍这种网络的拓扑结构和若干学习算法及其在语音识别和图像理解领域的成功实例.     

Global Robust Exponential Stability of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the equilibrium point of interval neural networks with delays are obtained. The delayed Hopfield network, Bidirectional associative memory network and Cellular neural network are special cases of the network model considered in this Letter. This revised version was published online in June 2006 with corrections to the Cover Date.     

Improved Global Robust Stability for Interval-Delayed Hopfield Neural Networks

A modified form of a recent criterion for the global robust stability of interval-delayed Hopfield neural networks is presented. The effectiveness of the modified criterion is demonstrated with the help of an example.